The USB-C port on the steam deck dos dual role power delivery so can output a max of 7.5 I believe. (You can prove this by charging your smart phone with it.)

So you have to power the screen and hub thingy within that 7.5 watt power budget. I suspect for long-term reliability, you'd be better off having a separate battery pack for the screen. Or only use the 2nd screen when plugged into AC/Mains.

But you could try it without all that with a tiny hub like this:

https://www.amazon.com/Twelve-South-Ultra-Thin-Tablets-Laptops/dp/B09C9W6SCC

Has only the ports you need and nothing else. Whatever hub you get, make sure it offers "passthrough" charging. so you can charge the deck while playing.